Problem: The sum of $6$ consecutive odd numbers is $204$. What is the fourth number in this sequence?
Call the first number in the sequence $x$ The next odd number in the sequence is $x + 2$ The sum of the $6$ consecutive odd numbers is: $x+ (x + 2)+ (x + 4)+ (x + 6)+ (x + 8)+ (x + 10) = 204$ $6x + 30= 204$ $6x = 174$ $x = 29$ Since $x$ is the first number, $x + 6$ is the fourth odd number. Thus, the fourth number in the sequence is $35$.